Answer to Question #209174 in Physics for hamza`

Question

Compute the extension in length of a wire 530 cm long and a diameter of 0.25 cm. When the body of mass 540 gm is applied vertically. The young modulus of given wire is 5x109 Dyne/cm2.

Answer 1

The stress in the wire:

$$\sigma=\frac FA=\frac{mg}{A}=\frac{4mg}{\pi d^2}.$$

Young's modulus in terms of stress and strain:

$$E=\frac\sigma\epsilon,\\\space\\ \epsilon=\frac \sigma E=\frac{\Delta l}{l},\\\space\\ \Delta l=l\frac\sigma E.$$

Substitute the stress:

$$\Delta l=l\frac{4mg}{\pi d^2E}=1.1\text{ cm}.$$

Do not forget to convert all units to SI!